Wednesday puzzle (don't mention the war!)

[GHA EFM]

I think I understand, now...

 

You should switch.

 

Let's say that Box A contains a goat, and Box B contains a goat, whilst Box C contains a car. One is more likely to pick a box with a goat in it, because there are more goats than cars.

 

Therefore, if you pick Box A, the quizmaster will open Box B to reveal the goat. If you pick Box B, the quizmaster will open Box A, and reveal a goat. Therefore, due to the likelihood that you will originally pick a goat, and the second goat is shown to you, you should then switch.

 

The technical answer is as follows:

 

Quote:

• The Monty Hall puzzle. This is based on an old American game-show in which contestants (as the story is now told) were offered a choice of three boxes. Open the correct one, and you won a car; open either of the others, and you won a goat. There was a twist. After the contestant had chosen, but before the box was opened, the host opened one of the other boxes to reveal a goat. Then he asked if the contestant wanted to stick with his first choice, or change his mind and open the third box instead. Question: is it a good idea to change your mind, a bad idea, or does it make no difference?

 

Almost everyone thinks it makes no difference. Once one of the goats has been revealed, you think, the chance that you have chosen a car improves from one in three to one in two—so it can’t make any difference to switch. Choose the other box, and the chance of winning is still one in two.

 

Wrong. It makes sense to switch: if you do, you double your chance of winning the car. The point is, your chance of winning the car was one in three to begin with—and after Monty reveals a goat, the probability that your box has the car is still just one in three. Because Monty’s choice was not random (he didn’t open just any box, he revealed a goat) the remaining probability of two-thirds gets squeezed, as it were, into the third box. So if you switch, your chance of winning goes up from one in three to two in three. Discussions of this point sometimes turn violent, so the diagram below may prove useful. It shows the full “probability tree” for the problem. Reading from left to right, you can trace every possible outcome, and its associated probability, under each of the two regimes—“don’t switch” and “switch”.

[Rob_the_Saint]

zzzzzzzzzzzzzzzzzzzzzzzzzzzzzz <img src="/forums/images/graemlins/wink.gif" alt="" />

[AFF]

Dull it isn't.

 

 

[MK James]

And while were talking probability - we've got more 20 times more chance of being taken out by a comet or asteroid than winning the lottery.

 

And yet I still do it <img src="/forums/images/graemlins/confused.gif" alt="" />

[Colin Zeal EFM]

If you buy a ticket at 9am on Monday, there is a higher probability of dying before the draw is made on Saturday night, than there is of winning it.